Good to consult a physiotherapist.. Will help for sure.. Duration depends on the grade of weakness.

The cause of external rotator weakness needs to be identified first and only then  rehabilitation can be started. Number of days will depend on factors such as diagnosis,age,current muscle strength etc

Seated Strengthener With Pulley The "cable seated hip external rotation" exercise, as explained by ExRx.net, targets all the major muscles in external rotation of the hip. Sit on a bench next to a weighted pulley positioned at ankle height. Place both feet on the floor hip-distance apart. The lower and upper halves of the legs should form right angles. Strap the pulley onto one ankle. Slightly lift the weighted leg, maintaining a 90-degree angle. Carefully swing the foot of the weighted leg behind the other one. Complete 10 to 12 reps, switch the weight to the other leg, and repeat. Side-Lying Strengthener With Band The "clamshell" also targets the external rotators, with emphasis on the gluteus medius. For this exercise, you’ll need a looped resistance band. Place the resistance band around your thighs, just above your knees. Lie on your right side with your knees bent and stacked. Place your right elbow under your head for support and your left hand on your hip. Lift your left knee off your right knee -- opening your knees into a clamshell. Complete 10 to 12 reps and repeat on the other side.

Consult a physiotherapist near by you Physiotherapy will strengthen your weak muscles. About the sittings you will come to know after the assessment of hip joint muscles.